A world where family is decided not by blood ties but by who takes it on
First, the definitions of 'motherhood' and 'family' will be rewritten wholesale, and I think a society will emerge where family is determined not by blood ties but by 'who takes in the child behind the door.' States and corporations will hold the rights to manage the door, and politics and business surrounding 'how many people to send to which region' and 'who should raise them' will develop at an extreme level. As a countermeasure to that, a counterculture like a commune that voluntarily goes to adopt the door's children will also be born.